Logica Universalis - Join the Logica Universalis Webinar 2024!
The Logica Universalis Webinar is a World Seminar Series connected to the journal Logica Universalis, the book series Studies in Universal Logic and the Universal Logic Project. It is an open platform for all scholars interested in the many aspects of logic. The project started in 2021. Click here to access the webinar series of past editions.
The LUW 2024 series starts with an "extraordinary" session: LUA celebration of the sixth World Logic Day. The celebration will be held from Cusco (Peru) during SALOME 1: the first South American LOgic MEeting, Jan 14, 2024.
The sessions take place on Wednesdays at 4pm CET. They are held via Zoom through the platform Cassyni and are free to attend. Please register and subscribe in advance.
Registration is now open!
Please note that you will be required to register before subscribing to the webinar series. You will be automatically directed to the registration page or click here.
Video recordings of the seminars are uploaded on the Cassyni platform.
Each session of the webinar is chaired by a member of the editorial board of the journal Logica Universalis (LU), the book series Studies in Universal Logic (SUL) or an organizer of an event of the Universal Logic Project (ULP). Sessions will start with a short presentation of a logical organization related to the region of the speaker or the topic of the talk. The talk (30 min) will focus on a recently published paper in LU, on a book in SUL, on an event or on the ULP. Talks are followed by a discussion (15 min).
Webinar Schedule
Speakers and Abstracts
February 14, 2024 – Til Eyinck (University of Cologne, Germany) –
Should We Embrace Impossible Worlds Due to the Flaws of Normal Modal Logic?
Chair: Ahti-Veikko Pietarinen, Editorial Board LU
Associate Organization: Women in Focus. Rethinking Philosophy and History of Mathematics and Physics presented by Jasmin Özel
Some philosophers advance the claim that the phenomena of logical omniscience and of the indiscernibility of metaphysical statements, which arise in (certain) interpretations of normal modal logic, provide strong reasons in favour of impossible world approaches. These two specific lines of argument will be presented and discussed in this paper. Contrary to the recent much-held view that the characteristics of these two phenomena provide us with strong reasons to adopt impossible world approaches, the view defended here is that no such ‘knock-down arguments’ do emanate on those grounds. This is not to rule out that there cannot be any other good reasons for assuming impossible world semantics. However, the discussion of a further argument for impossible worlds will suggest that different attempts to argue for them likely present intertwined problems.
-----
February 28, 2024 – Lin Chen and Xuefeng Wen (Sun Yat-sen University, China) –
On the transitivity of Logical Consequence without Assuming Monotonicity
Chair: Caroline Pires Ting, International Relations of LUA
Associate Organization: Institute of Logic and Cognition presented by its director Hu Liu
We generalize Ripley’s results on the transitivity of consequence relation, without assuming a logic to be monotonic. Following Gabbay, we assume nonmonotonic consequence relation to be inclusive and cautious monotonic, and figure out the implications between different forms of transitivity of logical consequence. Weaker frameworks without inclusiveness or cautious monotonicity are also discussed. The paper may provide basis for the study of both non-transitive logics and nonmonotonic ones.
-----
March 13, 2024 – Andrew Schumann (University of Information Technology and Management in Rzeszow, Poland) –
Stoic Sign-Inference and Their Lore of Fate
Chair: Srećko Kovač, Editorial Board LU
Associate Organization: Department of Cognitive Science and Mathematical Modelling, University of Information Technology and Management, presented by Jerzy Król
The Stoics are traditionally regarded as the founders of propositional logic. However, this is not entirely correct. They developed a theory of inference from signs (omens). And their theory became a continuation of the logical technique of Babylonian divination (in particular, of Babylonian medical forecasting). The Stoic theory was not so much propositional logic as it was a technique of propositional logic for databases consisting of IF-THEN expert rules. In the Babylonian divination, each event has a positive or negative value and all events are connected to each other. The Stoics also developed this idea and proposed a special modal logic in which logical determinism is considered an axiom. The paper reconstructs the sign-inference of the Stoics, as well as their modal logic. In particular, two Stoic squares of oppositions are proposed (for signs and for modal operators), which differ markedly from Aristotle's square.
-----
March 27, 2024 – José M. Sagüillo (University of Santiago de Compostela, Spain) –
The philosophy of logic of John Corcoran
Chair: Francesco Paoli, Editorial Board SUL
Book presentation: Universal Logic, Ethics, and Truth Essays in Honor of John Corcoran (1937-2021), presented by the editors Timothy Madigan and Jean-Yves Beziau
This talk surveys the philosophy of logic of John Corcoran by focusing on some of its characteristic themes: his understanding of logic as formal epistemology articulating the ontic-epistemic distinction of classical metaphysics, the Socratic belief-knowledge distinction, and the Aristotelian truth-knowledge distinction; his conception of mathematical logic as instrumental when considering mathematical logics as models of underlying reasoning found in the practice of proof; his tireless search for a careful and successful communication in a community of thinkers eliminating ambiguity of key terms and embracing ethical values; his discussion of argumentations and logic as a philosophical realization of the previous dichotomies, allowing precise definitions of key concepts, such as, argument, argumentation, proof, deduction, fallacy, and paradox; finally, his recovering and articulation of the XIX century information-theoretic conception of validity, exploring its heuristic power in the study of omega arguments and suggesting the existence of different paradigms of logical consequence equally entrenched in the theory and practice of logic.
-----
April 10, 2024 – Henri Prade (Toulouse Institute of Computer Science Research, France), Didier Dubois (Université Toulouse III - Paul Sabatier, France), Agnès Rico (Claude Bernard University Lyon 1, France) –
Modern vs. classical structures of opposition: A discussion
Chair: Sayantan Roy, Assistant Editor LU
Associate Organization: ADRIA-IRIT, CNRS presented by Didier Dubois
The aim of this work is to revisit the proposal made by Dag Westerståhl a decade ago when he provided a modern reading of the traditional square of opposition and of related structures. We propose a formalization of this modern view and contrast it with the classical one.We discuss what may be a modern hexagon of opposition and a modern cube, and show their interest in particular for relating quantitative expressions.
-----
April 24, 2024 – Ori Milstein –
Why the hexagon of opposition is really a triangle: logical structures as geometric shapes
Chair: Arnon Avron, Editorial Board LU
Associate Event: World Congress on the Square of Opposition presented by Pablo Villalobos Morera and Lorenzo Boccafogli
This paper suggests a new approach (with old roots) to the study of the connection between logic and geometry. Traditionally, most logic diagrams associate only vertices of shapes with propositions. The new approach, which can be dubbed ’full logical geometry’, aims to associate every element of a shape (edges, faces, etc.) with a proposition. The roots of this approach can be found in the works of Carroll, Jacoby, and more recently, Dubois and Prade. However, its potential has not been duly appreciated, probably because of the complexity of the diagrams in these works. The following study demonstrates how the Hexagon of Opposition can be represented as a triangle and Classical Logic as a tetrahedron (rather than a rhombic dodecahedron). It then applies the approach to modal logic, extending the tetrahedron for the logic KT into a dipyramid and a cube for KD, and finally an octahedron for K. Some possible directions for further research are also indicated.
-----
May 15, 2024 – Takaharu Oda (Southern University of Science and Technology, China) –
The Buddhist Sengzhao’s Roots in Daoism: Ex Contradictione Nihil
Chair: Caroline Pires Ting, International Relations LUA
Associate Organization: Asian Pragmatism Network presented by Jason Van Boom
Sengzhao (c.374–414) was a Chinese Neo-Daoist who converted to Mah¯ay¯ana Buddhism, and few people doubt his influence on Chinese Buddhist philosophy. In this article, provided his Neo-Daoism (xuanxue) and Madhyamaka Buddhism, I will present how Sengzhao featured a symbolic meaning of ‘void’ (´s¯unya) as rooted originally in Daoism. The Daoist contradictions, in particular between ‘being’ (you) and ‘nothing [non-being]’ (wu), are essential to the development of his doctrine of ‘no ultimate void’ (不真空論, Buzhenkonglun). To understand what Sengzhao meant by ‘void’, which is in denial about the ultimate reality, I broach a notion of nihil (‘nothing’ but also ‘no value’) that bears on his discursive practice. In this light, I formulate a Daoist argument for contradictions and ECN (ex contradictione nihil – nothing follows from contradictions) from Laozi’s Daodejing. Furthermore, I elaborate on Sengzhao’s defence of ECN in his Buzhenkonglun. Reconstructing his negative approach to contradictions within the scope of the four-valued expressions (catus.kot.i) in the Madhyamaka tradition from N¯ag¯arjuna, I consider a likely objection that a fifth value such as the ineffable may be inferred as void. Instead of subsuming the ineffable value under his discourse, I finally endorse Sengzhao’s purpose of linguistic and conventional approximation of the ultimate reality as silence. As such, I conclude the significance of void in Sengzhao’s denials via contradictions (ECN), i.e. an early philosophical peak of Chinese Buddhism from Daoism.
-----
May 29, 2024 – Oksana Cherkashina (Moscow State University, Russia) –
A 32-vertex generalization of the logical square: "Logical Lantern" for propositions in V.I. Markin's Universal language for traditional positive syllogistic theories
Chair: Ioannis Vandoulakis, Vice-President of LUA
Associate Organization: International Laboratory for Logic, Linguistics and Formal Philosophy presented by the Laboratory Head Elena Dragalina-Chernaya
In this talk is constructed an analogue of the square of opposition for propositions about logical relations between two non-empty sets. Unlike the classical square of opposition, the proposed scheme uses all logically possible syllogistic constants, formulated in V.I. Markin’s universal language for traditional positive syllogistic theories. This scheme can be called „Logical lantern”. The constructed scheme, making it possible to visually see the logical relations among propositions about relations between two nonempty sets, allows us to suggest considering logical relations not discussed previously: many-place Aristotelian-like logical relations among propositions: exhaustive n-place contrariety and exhaustive n-place subcontrariety.
-----
June 19, 2024 – Saloua Chatti (University of Tunis, Tunisia) –
The Oppositions of Categorical Propositions In Avicenna’s Frame
Chair: Jean-Yves Beziau, Editor-in-Chief LU
Associate Organization: Pan African society for logic, presented by its founding members Mohammed Almisbkawy and Omar Karam
The aim of this paper is to analyse categorical propositions and their oppositional relations in Avicenna’s frame. For Avicenna’s expression and conception of categorical propositions is different from those of the authors who preceded him, due to the various conditions he adds to these categorical propositions. These additions make the oppositional relations richer and give rise to many more figures than a simple square.
Our analysis exhibits some of these figures by relating all kinds of quantified propositions in various ways. We thus find many squares of oppositions, several octagons, two hexagons and many complex figures which are different from each other and have specific and original structures, due to the propositions they contain. The hexagons are of Blanché’s kind, but one of them is asymmetric. Some octagons are of Buridan’s kind, but one of them is very unusual and seems to be a reversal of Buridan’s octagon. These octagons can also be replaced by cubes, which are three dimensional figures having the same number of vertices.
-----
July 10, 2024 – Fabien Schang (Université de Lorraine, France) –
Quantifying Statements (Why ‘Every Thing’ is Not ‘Everything’, Among Other ‘Thing’s)
Chair: Sayantan Roy, Assistant Editor LU
Associate Organization: Archives Henri Poincaré presented by Andrei Rodin with the participation of Frida Trotter, publishing editor of Publications des Archives Henri Poincaré Publications of the Henri Poincaré Archives
The present paper wants to develop a formal semantics about a special class of formulas: quantifying statements, which are a kind of predicative statements where both subject- and predicate terms are quantifier expressions like ‘everything’, ‘something’, and ‘nothing’. After showing how talking about nothingness makes sense despite philosophical objections, I contend that there are two sorts of meaning in phrases including ‘thing’, viz. as an individual (e.g. ‘some thing’) or as a property (e.g. ‘something’). Then I display two kinds of logical forms for quantifying statements, depending on how these ‘thing’s are ordered into a whole prediction. Finally, an algebraic semantics is proposed for the finite set of quantifying statements to order these into a (fragmentary) dodecagon of logical relations. The corresponding Sub-Model Semantics (hereafter: SMS) aims to update the usual theory of opposition whilst leading to a research program for other kinds of statements like categorical and even modal propositions.
-----
July 24, 2024 – Ricardo Sousa Silvestre (Federal University of Campina Grande, Brazil) –
The Logic of God: A Pluralistic Representational Theory of Concepts
Chair: Jean-Yves Beziau, Editor-in-Chief LU
Associate Organization: LARA - Logic And Religion Association presented by its president Agnieszka Rostalska
In this paper I present a formalization of the theory of ideal concepts applied to the concept of God. It is done within a version of the Simplest Quantified Modal Logic (SQML) and attempts to solve three meta-problems related to the concept of God: the unicity of extension problem, the homogeneity/heterogeneity problem and the problem of conceptual unity.
-----
August 14, 2024 – Kirill Yankov, Alex Citkin, Ioannis Vandoulakis, Tatiana Denisova –
In memory of the distinguished logician, philosopher and political activist V.A. Yankov (1935 - 2024)
Chair: Sergei Odintsov, Editorial Board LU
Book presentation: V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics, presented by the editors Alex Citkin and Ioannis Vandoulakis
This session consists of four short presentations:
A brief overview of the biography of V.A. Yankov (Kirill Yankov)
Yankov’s contributions to propositional logic (Alex Citkin)
The talk I will present two most significant contributions by V.A Yankov: the Yankov Logic and Yankov characteristic formulas.
V.A. Yankov’s Contribution to the History and Philosophy of Mathematics (Ioannis Vandoulakis)
The talk will present three significant contributions of V.A. Yankov to the History and Philosophy of Mathematics:
By inviting A.A. Markov, the founder of the Russian school of constructivism and his teacher, to respond to Heyting’s fictional persons “Class,” “Form,” “Int,” “Pragm,” and “Sign,” which represent classical mathematics, formalism, intuitionism, pragmatism and significism, respectively, when he edited the Russian translation of Heyting’s Intuitionism. This response is the only historical record of Markov’s views on Brouwer’s intuitionistic mathematics and logic.
His appraisal of A.S. Esenin-Vol’pin’s program of ultra-intuitionistic foundations of mathematics stated in his commentary published in a volume dedicated to Esenin-Vol’pin by Finn and Daniel’ in 1999, in which he also included three less known and hardly accessible works of Esenin-Vol’pin [1967, 1971, 1999] devoted to the theory of modalities, deontic logic, the theory of disputes and the logic of trust.
His novel interpretation of the rise of mathematics and mathematical proof in ancient Greece. It is formulated by considering the development of the early Greek philosophers’ ontological conceptions.
V.A. Yankov’s existential research program (Tatiana Denisova)
In this talk, I will discuss the least known and, at the same time, the most controversial research program proposed by V.A. Yankov, namely his philosophical conception of the existential history of human thought, which is based on the idea of reconsidering the WHOLE history of human thought from an existential perspective. That means that the whole history of philosophy, regardless of the immediate subject of philosophers’ reasoning, is required to be reinterpreted as a history of “existential types”, i.e., as a history of the changes in the human’s self-understanding and the correlated changes in human’s understanding of the general picture of the world.
-----
August 21, 2024 – Jean-Yves Beziau (Universidade Federal do Rio de Janeiro, Brazil) and Alessio Moretti (Università degli Studi eCampus, Italy) –
Smurfing the Square of Opposition
Chair: Sayantan Roy, Assistant Editor LU
This session is about the Special Issue of Logica Universalis (vol 18, nos 1-2, 2024) dedicated to the 7th World Congress on the Square of Opposition Leuven 2022. We discuss the history of the revival of the theory of opposition, with its emerging paradigms of research, and the related events that are organized in this perspective, including the latest one in Leuven in 2022.